The win ensured that the two World Cup winners will make their final appearances for Tigers in the final at Twickenham on May 28 before hanging up their boots.
Defeat means that Wasps, champions for the last two years via the semi-final play-off route, will have to go that way again in order to make it three in a row.
The day belonged to Tigers, and the crowd rose to pay tribute to Johnson – captain of English rugby's greatest day – and flanker Back following an overwhelming performance.
Top-quality tries by England scrum-half Harry Ellis, centre Daryl Gibson, winger Geordan Murphy, Back and replacement Dan Hipkiss, plus 20 points from the reliable boot of fly-half Andy Goode, gave Leicester the win.
Goode converted four of the five tries, landed three out of four penalties and also kicked a drop goal on the stroke of half-time.
All Wasps had to show in return was an early penalty from full-back Mark van Gisbergen, which briefly levelled the scores early in the first half, and a late consolation try by left-wing Tom Voyce, converted by van Gisbergen.
Wasps showed early promise but a stunning try by Ellis put Leicester in control and they never loosened their grip on the game.
Lions selection Ellis, who outshone World Cup-winner Matt Dawson, took a fine pass from flanker Henry Tuilagi just inside the Wasps half and in the absence of support, he accelerated through a gap to score with a terrific turn of pace.
Tuilagi's day turned sour four minutes later when he suffered a suspected broken leg as Voyce hauled him back two metres short of the try line.
But nothing was stopping Leicester and they struck again in the 32nd minute.
Forwards Julian White, Johnson and George Chuter carved up the Wasps' rearguard with a close passing move before Tigers whipped the ball out wide for Murphy to send Gibson over in the left-hand corner.
Murphy scored the third try three minutes after the interval to extend the lead to 33-3, snatching an interception and racing 70 metres for a runaway try between the posts.
Fittingly it was Back who scored the fourth try – his 125th for Tigers – when he pounced on a loose ball, kicked ahead and easily won the chase to touch down in the right-hand corner.
The try crowned another impressive performance by a 36-year-old who showed he still has plenty to offer the British Lions when he becomes their oldest tourist on this summer's trip to New Zealand.
There was more to come with Goode punishing Wasps by grabbing another interception to send Hipkiss in for their fifth try.
The way Leicester bounced back from last week's Heineken Cup defeat by Toulouse will make them firm favourites to send Johnson and Back, who is taking up a full-time coaching role at Welford Road next season, into retirement with one final glory day at Twickenham in a fortnight's time.
For Leicester:Tries: Ellis, Gibson, Murphy, Back, HipkissCons: Goode 4Pens: Goode 3Drop goal: Goode
For Wasps:Try: VoyceCon: Van GisbergenPen: Van Gisbergen
Leicester Tigers: 15 Sam Vesty, 14 Geordan Murphy, 13 Ollie Smith, 12 Daryl Gibson, 11 Austin Healey, 10 Andy Goode, 9 Harry Ellis, 8 Louis Deacon, 7 Neil Back, 6 Henry Tuilagi, 5 Ben Kay, 4 Martin Johnson (captain), 3 Julian White, 2 George Chuter, 1 Darren Morris.Replacements: 16 James Buckland, 17 Michael Holford, 18 Brett Deacon, 19 Will Johnson, 20 Scott Bemand, 21 Dan Hipkiss, 22 Alesana Tuilagi.
London Wasps: 15 Mark Van Gisbergen, 14 Paul Sackey, 13 Ayoola Erinle, 12 Josh Lewsey, 11 Tom Voyce, 10 Alex King, 9 Matt Dawson, 8 Lawrence Dallaglio (capt), 7 Tom Rees, 6 Joe Worsley, 5 Richard Birkett, 4 Simon Shaw, 3 Will Green, 2 Phil Greening, 1 Tim Payne.Replacements: 16 Trevor Leota, 17 Alistair McKenzie, 18 John Hart, 19 Martin Purdy, 20 Warren Fury, 21 James Brooks, 22 Joseph Mbu.
Kick-off: 15.00 (14.00 GMT)Referee: Tony Spreadbury Touch judges: Paul Emerson, Andy Watson